2024-02-15 14:09:15
Understanding the brain mechanisms that underlie our interaction with the world is one of the major goals of today’s scientific community. But this naturally comes up once morest the complexity of the human brain, pushing many researchers to take a step aside by first studying these mechanisms on simpler organisms. As Claude Bernard stated in his Introduction to the Study of Experimental Medicine (1865),
“The happy choice of an animal […] is often enough to resolve the highest general questions. »
And there are organisms which prove particularly interesting from this point of view: the worm Caenorhabditis elegans (C. elegans). Studying and modeling the nervous system constitutes a window onto the nervous system of vertebrates, and ultimately of humans.
Approximately 1 mm in length, the C. elegans worm is one of the simplest multicellular organisms, making it a preferred model animal in biology.
MA Hanson/Wikimedia, CC BY-SA
C. elegans: a worm that has already won a Nobel Prize
C. elegans is a nematode that has become a star of laboratories since its introduction in the 1970s by the eminent biologist Sydney Brenner, pioneer of molecular biology. This small worm, measuring 1.3 mm in size and 0.08 mm in diameter, lives in moist soils, thin films of water, or even in decomposing plants and feeds on micro-organisms. There are no females of this species, and the hermaphroditic form largely predominates over the male sex.
Sydney Brenner, visionary, saw in C. elegans an ideal organism for the study of important and diverse biological processes taking place in all living organisms, even the most complex ones such as humans. The awarding of two Nobel Prizes in medicine or physiology (2002 and 2006) and a Nobel Prize in chemistry (2008) for work carried out on the worm will prove him right. However, none of these prizes were obtained for studies on its nervous system, although it is very rich, combining simplicity and complexity.
A small but strong worm
The apparent simplicity of its nervous system also quickly made it an ideal organism for the study of physiological mechanisms related to the generation of behavior. Indeed, its nervous system is made up of precisely 302 neurons, and around 7000 synaptic connections for its hermaphrodite version. By comparison, humans have around 100 billion neurons, for an estimate of 10,000 connections per neuron. The connectome of C. elegans – the set of connections that are established between all neurons – was completely described in 1986, and updated many times since. It is currently the only organization in the world for which we have such complete and precise information.
During its three days of life, its nervous system allows it to move, eat, sleep, defecate, reproduce, etc. But it also allows the generation of a wide variety of richer and more complex behaviors and capacities: chemotaxis (behavior of attraction or repulsion towards chemical substances), learning, development of strategies to escape predators, or even social abilities. So many behaviors made possible by such a simple brain… Simple, but perhaps only in appearance.
Indeed, the study of the microscopic components of its nervous system reveals a much more complex and extensive machinery than initially imagined. In particular, we observe great similarities, at different scales, in the functioning of its brain and that of more complex vertebrates of which we, humans, are a part. This latter property makes it an ideal little window into the study of the vertebrate nervous system. If the classic tools of biology allow the exploration of these characteristics, modeling and computer simulations can also play a crucial role in their understanding.
A modeling challenge not as simple as it seems
The modeling in which we are interested consists of constructing equations to reproduce the behavior of the worm’s neurons. Modeling always consists of a game of compromise between realism and simplicity. The model must be realistic with regard to the phenomenon, or a set of its characteristics deemed relevant, that we are trying to describe. This correspondence of the model to reality depends in particular on the scale at which we place ourselves. The finer the scale, the more precise data is required, which is sometimes technically difficult to obtain. But it must also be simple enough to allow its study and computer simulation in order to be able to make predictions, otherwise the model would be useless.
In the case that interests us, the idea is to build models faithful to the physiology of neurons. Neurons being cells, the intracellular environment is separated from the extracellular environment by an impermeable membrane. Raincoat ? Not quite. Indeed, small channels located all along the neuron allow certain charged particles (ions) to circulate between the inside and outside of the neuron. It is the movement of these ions which is at the origin of the electrical activity of a neuron. Translating this activity into mathematical language therefore involves describing the movements of these ions on either side of the membrane.
In the case of neurons of C. elegans, one of the difficulties comes from the lack of knowledge of the ions involved, the charged particles which circulate between the inside and the outside of the neuron and responsible for the electrical signal. This problem largely comes from the small size of the neurons and the difficulty of dissecting a millimeter-long worm without killing it. Without precise information on the components responsible for the behavior of a neuron, the task of modeling its behavior immediately becomes more difficult. One way to overcome these difficulties is to develop computer algorithms and mathematical methodologies to hypothetically determine certain ions involved, thus making the construction of the model possible. These developments have been the subject of thesis at the Le Havre applied mathematics laboratory (LMAH).
Building models of this type requires going through different stages, from neurophysiology laboratories to mathematics laboratories which may require specific measurements. It is therefore necessary to design the manipulations on the worms to determine a minimum of parameters necessary for the construction of the models. Thus, modeling work of this type fundamentally requires interdisciplinary work in which researchers from different disciplines (neurophysiology, mathematics, computer science) are involved. As Alexandre Grothendieck, considered one of the greatest mathematicians of the 20th century, writes so well in his diary Harvests and Sowing,
“It is to the extent that complementary points of view of the same reality are combined, where our “eyes” multiply, that the gaze penetrates deeper into the knowledge of things. »
Today, where are we?
Despite the difficulties in dissecting the neurons of this little worm, we were able to collect certain precise data on the functioning of its neurons thanks to measurements carried out by neurophysiologists from Rockefeller University.
Part of the worm’s neurons C. elegans is now modeled quite precisely. This step of modeling neurons is necessary to advance in understanding the functioning of the nervous system. However, it is not sufficient, because it is ultimately the interaction between its different neurons and the environment which determines the macroscopic behaviors of the worm and which is of interest to the scientific community.
Thus, other researchers are working on modeling the behavior of the worm, but without taking into account biological elements at the neuronal scale. It therefore remains to build a model integrating these different scales: starting from the behaviors of neurons at the microscopic scale to reproduce the observable behaviors of the worm at the macroscopic scale.
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